{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "mode_regression_nn.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "last_runtime": {
        "build_target": "//learning/brain/python/client:colab_notebook_py3",
        "kind": "private"
      }
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bZCvVbB1gbGH",
        "colab_type": "text"
      },
      "source": [
        "***Copyright 2020 Google LLC.***\n",
        "\n",
        "Licensed under the Apache License, Version 2.0 (the \"License\");"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "X_Kwbd8GgW6k",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#@title Default title text\n",
        "# Licensed under the Apache License, Version 2.0 (the \"License\");\n",
        "# you may not use this file except in compliance with the License.\n",
        "# You may obtain a copy of the License at\n",
        "#\n",
        "# https://www.apache.org/licenses/LICENSE-2.0\n",
        "#\n",
        "# Unless required by applicable law or agreed to in writing, software\n",
        "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "# See the License for the specific language governing permissions and\n",
        "# limitations under the License."
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wng8KpSARKuG",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import tensorflow.compat.v2 as tf\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T37b-H9BRRLJ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "tf.enable_v2_behavior()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jGTee7vtdEtj",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Mode as a function of observation\n",
        "def f(s):\n",
        "  return np.sin(s*2*np.pi/100.)/2."
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kQrsv8kNdM5-",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "N = 100\n",
        "s = np.random.uniform(-100, 100, size=N)  # observations between -100 and 100\n",
        "a = np.random.uniform(-1, 1, size=N)  # Actions between -1 and 1"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VpkmOcwrdf6G",
        "colab_type": "code",
        "outputId": "361a5b61-3c6b-4a34-a071-42e1bfe123a6",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1568423233252,
          "user_tz": 420,
          "elapsed": 289,
          "user": {
            "displayName": "Dan Abolafia",
            "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mAQmxyT8biPkQeDgz5lf2ocSzJsOqH8BqBuLz1a=s64",
            "userId": "05741471333872541970"
          }
        },
        "colab": {
          "height": 51
        }
      },
      "source": [
        "P = 0.2\n",
        "y = -100*np.abs(a - f(s))**P\n",
        "y /= np.max(np.abs(y))\n",
        "print(np.max(y))\n",
        "print(np.min(y))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "-0.19769162598050274\n",
            "-1.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PlFJsBWleHZu",
        "colab_type": "code",
        "outputId": "f86eb1bd-b14e-4e90-e483-8160f854d882",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1568423233792,
          "user_tz": 420,
          "elapsed": 521,
          "user": {
            "displayName": "Dan Abolafia",
            "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mAQmxyT8biPkQeDgz5lf2ocSzJsOqH8BqBuLz1a=s64",
            "userId": "05741471333872541970"
          }
        },
        "colab": {
          "height": 286
        }
      },
      "source": [
        "plt.scatter(s, a, c=y)\n",
        "plt.plot(np.sort(s), f(np.sort(s)))\n",
        "plt.plot()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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VqJUK+sZFMKxr9J07S0hIAJCw6Vi5qnpQWjTp4LF0B0gkcSekI6ZKEOTbiN9nTWRPUiqX\n84tp3cKfEP/SWA6dwUhS5iVc1SrC/LwkA2olOHX4PItmrubMsQx8/BvxwPMD6TqojaPFkrAxFb0a\noggWoz9vgyiKHNp7jr83HEOtUtJ3WFvCWlqOXbAlJqMJmVxWb997SUFUEoVcRpfWzctcW7X/OO/+\nthGZIGASRZp4uDLv0ZE09WrkIClrN9oSPSknMnn1gXnoSkpXklfzipk1bQkFV0YxeJzkEVafGdwn\nhl37z1ncRcRGB1voYRlRFPnwzV/ZtjEJbYkBmUzgj58TGT+5N/c9YpsYGW2xnrycAhr7eaBSKzmx\n/xxzXl7G2WMZqNQKBjzQhYlv3lOuyFBdR1IQ1eR45iXe/nUD2psC5lJz8pj41c8kvDShXiXNqylJ\n+1P47I2fSTuTjag3IN6SM0pXYmDRzNUMGNNRim+ox3TuEEq/bi1Z//dxjCbz9WwA7708HLWq8lPR\n4X0p15UDlLqi67QGvp23kd6DW+Pt6241mU0mM1+98wtrvttW+k4LAkPHd2P1N1uuL3J0WgPrlu4g\nJ/MKb34z2Wpj1wYkBVFNlu88hP6WXEFmUeRKUQk7z5yna3gzB0lWu8hMzeH1R79Cey3xWQUJBXUl\negpyi/D0cbOjdLWfc1m5zPxpE4mn09GolNzTOYZnhnZBVQejeQVB4JVnBnHPkHbsOVjq5tq7SyQe\n7k5Vus/2v46js7ALkctlJG5PZtCoDtYSmSWzVrN2yTb0N43325ebMN/yHOu1BvZtPk5W2mX86lHV\nubr3lNUSsq8WYbYQQlKsNzBx+S808/Hk3cH9uKtZkF3kOZ+Tx4qdh8i8cpXO4U25u0MUTrXADffX\nRVsxVCItiSAIuFRxoqjvZOcX8tBHyyjS6hEBQ4mO5VsPkXLpCp9NGuFo8apNeKgf4aF+1e6vVisQ\nZAKiqez7JwgCKrX1nnmTycxvX22+vlO4+bqlXGFKlYLMlOx6pSCk/Xw16dmyORoLqzgRMAlwNvcK\nT/zwK2dycm0uy/aTKdzz8Xd8v+0g648kM2v134z+eAkFJVqbj30nUk5lYTLetNqSl884q3ZSMnR8\nV1Rqab1yMyu2lu5Sb56KdAYju06mknrpisPkcjR9h8VazFxsNot07GG9wkN6rb7MzqEMFozSep2B\n4LAmVhu/NiApiGoyokM0gZ7uqBU3JjURMKu4/q3qjSYW7rFt7QKT2cxry9ehNRgx/rPtLdEbuJh3\nlW+3OL5uQsvYYJSqm15mmaz0X0pXXGqNkqEPdWXCK8McJGHt5dj5rHLHmABKuZyzF22/8KithLTw\n5fHnB6BSKXByVpVWp9MoeWPW/bi4aq630xbr+XHh3zw/Zi7/enwhOzcmVakinMZZjVcTy/XehVts\njGonJd2Gtcfbv345qEhLtmqiUSpYNmUcP+w+zM+JR0m5kodRISLetMM1iSKnsy/bVI6U7CuU6Muv\ncvQmE+sOJ/PsIMdmPh35SDfWrtiN0WC+/nKqXTR0GRDDpNeG4ezmJO0cKiAyyIe9yekYTGWVhMFk\npplv/ZqIKiIj4wrffLOVw0fSaNzYlQce6ET3bpGMGNeRHgOiSdx+GqVKzl3dI3B2UV/vp9MamDp2\nHhfSrqD/Jwjv+MFUhj/YmcdeqFy+N0EQePLde5n1zDfXj5kEAVQaFc/NeoD1y3dwbPcZnFw13D2h\nJ+Om1q48ctZAejNrgItaxWM94hjWPoo+c79GvOVFVsrltAu0rm/22dxclh89wuXiYvqGtqCNt185\ng9kN+Rxvg/Dy82D2T8/y1YzVHNp1BmcXNXeP78p9T/REXo8KHNmCcd1j+WHroTIKQqWQ0655AKFN\n6s85d0VkZubx5ORFaLUGzGaR7OyrfPCf1Vx8LJ/77rsLTy9X+g+Ptdh30+qDZGXcUA4A2hIDvy7e\nwYjxXWjsUzlPp65DYnH97mm+/+gPMs5m06J1EONfHEZ426b0GR1vld+zNiMpCCvg4+rC8JgoVh07\ngdZYapAVAI1CzqMdredRsfrkCV5e/ycGkwmTKLLuzGmivH1o4efFiczsMkZzJ6WCB7pafnnsTVBz\nH97+4jFHi1Hn8PN0Y9HU+/n3Dxs5nHIBlVzO8I6tmD6qp6NFswtLlmy/rhyuodUZ+OabrYwY0R7V\nbVxj92w5ed0N9mYUSjnH9qfSfWDrSsvRtmsEbbtaz7ZRl5AUhJV4d3BfQr08+XbvAQp1ejo2C+Ll\nPj1o4madTJVao4FXN6y/roAAig0GkrIv8XynzlzdrONyYTECYDSZGdY+iuEdWlllbAnHERnow+Jp\nYzGZzcgEod5G7FriyJF0y4kyBYGMjCs0b15x4TAvXzdkMsFif48GVBGupkgKwkrIZTIe7xTH453i\nbHL/AxcuILMwOZQYjWxJT+GPlx9jf0oG2QVFtGnahMDGlo1rEnUTuazh+ZP4+rmTkVneW8toNNH4\nDpP80LEdWf/r/jLxEoIg4ObuREyHEGuLWm9peE9dHcVJoazQA8NFpUQmE4gLDWJwbKSkHCTqBQ+M\n64z6FjuaSiWnc+cwPDycb9s3JLwJL/xnNM6uapxd1KidlASGePHBwseRNUBlW12s8k0lJCQQGRlJ\nWFgYM2bMKPf55s2b8fDwIDY2ltjYWN59991K95UopU2TJriq1OWuOymUjGstJbqTqH906BDC888P\nwM1Ng0ajRKmU07VrBK9W0iW6x6A2LNv2Ou9/9RifLn+aBaunEdCs/hv3rUmNj5hMJhNTpkxh/fr1\nBAUFER8fz/Dhw2nVquz5d/fu3Vm9enW1+kqATBBYOHIUD/38EwazCbMoYjKbGd+2Lb1Cmt/5BhIS\ndZBBA1vTv180WVkFuLtrcL0pzqEyqFQKoto2tZF09Z8aK4g9e/YQFhZGaGgoAGPHjmXlypWVmuRr\n0rchEuXjw64nJrH1fCr5Wi0dg4IJcJNyF0nUb+RyGTqDkcXLdlJYpKVb53A6xbeQEmLagRoriIyM\nDIKDb6TqDQoKYvfu3eXa7dy5k7Zt2xIQEMCHH35IdHR0pfvWJ05cLGDLyWwOnM/jcpGOK8UGCkoM\nRAe4MyI2kP6t/HC5TeCYUi6nT/NQO0osUZ8QRZHMfC1HM/I5llnAsYx8zl0uIrCRE+2aejK+UzN8\n3MofZTqSPxIO8dnnGzEYTZjNIn9tOUHb1sH85617pOy/NqbGCsKS4fRWV7z27duTmpqKq6sra9as\nYeTIkSQnJ1eq7zUWLFjAggULAMjOzq6p2HbFYDKz6lAm3+5M5VBaHgDNvV3wc1cT7uuKs0rBzjM5\nTF1xECelnP6t/BjZLoDu4T4opRdAogaIosjfyTnsOJ3DscwCjmbmk1dc6tkjE6CFjythPq5k5pcw\n569kvthyhjFxwUzqEUpw49sbgu3B1UItn36+Eb3+hnu3Vmvg8JE0tu1Mpme3SAdKV/+psYIICgoi\nLS3t+s/p6ekEBASUaePufiNqcciQITz99NPk5ORUqu81Jk2axKRJkwCIi7ONK6ktOJKez7QfDnL6\nUiGhPi68dXcrBsf408Sj7Fmq2SySmHqF3w5msObIBX4/lImns5KhbfwZERtIXDNPq/jAF+sMrNl/\nnOMZlwhv4s2wuChcNbVrxWgr8nIL2bnxOEaDkbt6tsQv0NPRItmUczlFvPX7Mf4+lY1SLhDZxI1B\n0U2IDnAnOtCDqCbuON2UJ+tcThFfbDnD8r3nWbrnPCPaBvBUrxaE+znuGPPg4TQUChl6fdnrJVoD\nm/4+cV1B5GRf5ejh86SczUbjpKJnnyj8A+r339ceCGJVsldZwGg0EhERwcaNGwkMDCQ+Pp6lS5cS\nHX2jXvPFixfx8/NDEAT27NnDvffeS2pqKiaT6Y59LREXF0diYmJNxLY5RpOZzzef4dONyXi7qnl3\nRDT9W/lVapLXG838fSqblYcyWZ90Ea3BzOCYJsy8tw3uNahYlZVXyAOzl1Ko1VGiN6JRKdAoFXz/\n/DiCvet3bp+tCUf48LUfS9NEmwFEHprSl/sm1r+oZKPJzGd/nWb+5jOoFDJe6B/Bg52aoq5kapML\n+SV8tfUcS3efp8RgYkArP/5vaCuaetl/R7E78SzvfPA7xcU3aQhRRACCAj0ZPrgtO7cmc/RwWmlQ\nnCgiEwSUchnPTBvE4LtrRzaB2kJV584aKwiANWvWMHXqVEwmExMmTOD1119n/vz5AEyePJk5c+bw\n+eefo1AocHJy4uOPP6ZLly4V9r0TtV1BpOQUMe2Hgxw4n8fwtgG8NyIGD+fqTexFOiPf7kzhoz9P\nEdBIw9wH2tMmqHqT+fRvV/PX4dOYbvqTywSB+LAgvnzq3mrdsy5QkFfM+D4zy6VuVmuUfLJsMs0j\n7V/L2FYYTWam/XCIVYcyGd42gP8bGoWve9U8f66RW6Tnmx0pLNp2DrlcYN6D7enSwtvKEt8eg8HE\nqAfmUFioK70giiDeKGGtMJjL1YVAFMEkolYp+P6XZ2nkKUVOX8MhCsLe1GYFsS05h8lL9iET4L2R\nMYyIDbTKffelXuHZpfvJLtTx0ZhYhre1fBR3O+565X9lSqReQyYI7Jv1XL2N1l3/6z7m/XsV2uKy\n5xQymcDoCd2ZUMnsnrUdk1nkhR8OsvJgJq8MaslTvVpY5b4pOUVMXJxISk4Rbw+P5qFO9q2WeDQp\ng1fe+AlRFNGW6BGvpc8wi8j0Zsrtyf9RIk5qBc9MG8TAoW3tKm9tpqpzZ/2cERzExuNZTPhmL0Ge\nTiRM7WE15QDQoZkna57vTrumnjy//ADfbD9X5XtUpABkMgGh/GtWbzCZzBYdIkRRLFvMqA5jMou8\n9OMhVh7M5KWBkVZTDgAh3i788nQXuod783+/HWXG2hNVqqtQU2JaBfLL0qd5eeogi5XcyiEIUPqP\n5ApbQyQFYSXWHrnAk9/tI8rfjeWTOhHQyPrlMxs5q1g84S76R/nx9qokFvx9pkr9h3SIRHXLObRS\nLqNf67Ba+SJpS/Ss+yWRue//zqpluygqrF6FvLt6Rt5Ydd6ESq2sUlbP2orZLPLKz4f55UAGL/SP\nYErvMKuP4a5R8tUj8TzYsSnzt5zhs42nrT7G7VCrlXTvGlE2TUZFj+w/OwiTWaRj13C7yFdfkZL1\nWYE/j13kmWUHiA1uxKLH4mtkSL4TGqWceQ+25/kVB/nPmhO4a5SMvatykaIvDOtBUtolzmblIooi\nMpmAv6c7/xrdx2byVpfL2QU8f//nFF7Voi3Wo3FS8t2cjcxeOrnK6RIa+7gz8aUhfDVrDSajGbNZ\nRKVWMOi+eFq2Db7zDWoxZrPIa78c4ad96TzfN5zn+tpuQpTLBN4bEYPOaOaTDadwUcuZ2N1+MTly\nuYyuncPYses0RqMZBAFRLiDcaoMQBFRygZdeH457NeucpyRn8cvibaSn5BDdvhkjH+qCVyVrSFQX\nURTZkHCEn1fspqhQR5fuEYx7uKtDbSiSDaKGbDqTxsSFh1C76undw8BTrboR42m9o6WKMJjMTPw2\nkW2nc/jq4Th6t/StVD9RFNl/LoPTFy4T4utJfIvgWrl7+ODF5Wz781hpgfh/EGQCbeKaM3PR49W6\nZ3pKDpv/OITRYKRLv2giYoKsJa5DMJtFXv/tKMv2nOfZPmG80D/CLunAjSYzzy0/wJojF/ngntaM\nq+QCxRrk5xcz9aVlZF3Kx2wWEQQBPy9XPF2dyLl0FR8fN+7q2IKBQ9rg2bh6qfb37zzNO88twaA3\nYjaLKJVy1E4q5qx4miZBja38G91g7ifrSFh1EO0/zhQKhYxGni58ueRJXN2q52hwK5KR2o4cunSR\ne+btwGwWcGp9DJnKiFqu5JP4++jhZ/sCI0U6I/cv2MmZS0WseLJTtb2baiMj495BW6Ivd10mE1h1\n4J0GX41OFEXeWHmUJbvO81SvFrw8MNKutSL0RjNPfpfI5lPZfDk+jn6t/Ow2tiiKHDx0nvTMK4SG\n+NAqKsBqv7soijw66EOyMvPKXBcEgR4DY3ht1lirjHMrl3OuMv7eORj0ZatSqtQKHnm8J2Me6myV\ncSQjtZ0wmUUmLtmNSadEHXEaQWVEBLQmA+8e+sMuRjwXtYKFj8bj5api0uJ9ZF/V2XxMeyGXW37h\nBZlQaoRswIiiyFu/H2PJrvM82SPU7soBQKWQ8flDHYgJ8GDqioOcvnTVbmMLgkC72GbcPSSW6FaB\nVv3d868Uk5td/ncRRZH9u6qChEdQAAAgAElEQVRm86sKyScvolSWP/HX64zsT6y6Q4q1kBRENZm9\n4RTZlxSomp9H7lZU5rMcXSF5+mK7yOHrpmHB+DiuFOt5dtl+jKb64ZXTe1gsSlXZXYJcIaNTr5YN\nPv/OrHUnWbwzlYndmvPq4JYOqzKnUcr5YnwHNEoZTyzeR76FEp91DY1TxfZDax3zWMLb2w2zhXdX\nJhNoEuC4k4GG/aZVk/VJWfzvr9M0CihA4Vs+L5QAOCtUdpOnVYA7/xnVml1nc5mZcMJu49qSCS8M\nJCS8CRpnFSq1AicXFf7BjXn2rZGOFs2hbDp5iXmbzzA2PpjXh0Y5vARpQCMn5j3YgbTcYl768ZBd\n3V9tgcZJRec+UeUWJ2qNknse7mqzcVtE+BEQ5Flu8aNUyhl1X7zNxr0TkhdTFTmbXcgLKw7SJsiD\n+wf58smJs5SYbqyc1DIFgwNjUMtt58lkidEdgjiYlseXW8/RM8KXbuH2jXi1Ns4uaj5b8RRH96Vw\n7lQWQSHexHYKbdDVwC4VaHnxh0O0bOLG28OjHa4crnFX88a8Orgl7/9xnG93pPBo17pdn2TqO/dw\nNf97jh1IRalUoNcb6T+iPbGdWrBqxR6cXFR07tUSlyrWprgdgiAwY/YDvP/Grxw/lo5cJsPJWcX0\n14bR7Da1t22NZKSuAkU6IyPnbudykZ5Vz3YjwEPDJ0kbWHJ2N0qZHIPZRHe/MGZ2GI3GzgoCQGsw\nMfjTrRhMZtZN7XHbtOESdQuzWeThhXtITM1l1TPdHJpAzxKiKPL4P151vz/TlZZNbOsSag8yz18m\nKzOPkDA/flq8jVUr9gCl7rYi8M6nD9I23vrK8EpuIUVFegICPa3uYSh5MdmQ1345zIq9aXz3eEe6\nht1YoRcYSkgpvIy/kwc+Gse+uHtTchnzxU4e6RzC28Nvn/RQou7w+eYzzEw4YXe30qqQU6hj0Oyt\neLmoWPlMVzRK63ia6Q1G/tiWxF97TuHqrGZ037bEtar6d7B7RzJfzN1IRloujb1cGf9YdwbfHXvH\nndiB3Wd4Z+pStLfYWJxd1Sz/6xVUqrqzEJO8mGzEtuQclu1J44nuoWWUA4C70ok2nkEOVw4A8SGN\nebhTM77dmUJiSq6jxZGwAmeyC/l4/UmGtG7C2PjaG9jn7apm1n1tOJl1lXmbrePxYzCaePL9Fcz+\nfjN7jp3nr73JTP/4NxatrFphscQ9Z3nvjV9IS72M2SySk32VeZ+t57ef7jxZ/vnbgXLKAQARDjvQ\nw8geSAqiEhTqjLzy82FCvV2Y1t/28Q015eVBLQnwcOLlnw+jNZju3EGi1iKKIm//fgyNUs47w2Nq\njd2hInpH+jIyNoDPN5++7voqiiKJOedZef4wZwqqVuxr/a6TnMvMRXtzwSC9kYUrd5FbUHlPwYVf\nbEKnK5uoUqc1sHjh36Vpwm+D4TbvkLGev1+SgqgEM9YeJzO/hFn3tbHattmWuKgVfHBPa85mF/Hp\nxmRHiyNRA9YevcjW5Bym94+odaVAK+L/hrXCRa3gX78cJbu4kKEbPueJ7Ut55+Aa7tn0JVN2rsBg\nrtzEumXfaUp05VfvSoWcgyfTKy1Teprl3bS2RE9x0e3jh3oPaW3R/dVkMtvEBlGbkBTEHdhxJocl\nu84zoWtzOjSzXZi9tekR4cOYuCAW/H2Woxn5jhZHohoU6428tzqJKH93u6fYrgnermr+NTiKPSm5\nPPzbWlILcyk26Sky6tGajGzLOsPC5J2VulcjNydkFnZNIuDuUnkvooAKqsupNUqcnG/vkt65V0s6\ndAlH46REEEChlKNSK5j29kicnOuG0q4ukoK4DXqjmX/9coQQL2deHFD3at++PrQVXi4qXvrpMAY7\nBdBt232ap1/+nvufWMCsuevIyi6wy7j1kf/9dZoL+VreGxGNoo4FB94XF0RcSCOOH1Nh0JeVXWs2\nsuLcvkrd554+bVFa2LU7qZW0a1n5XFqPPdkL9S1efRqNkgcf6XbHwEuZTMb/fXg/73z2IKMe6sy4\nJ3qy4Jdn6TWo7mcCvhNWeeoSEhKIjIwkLCyMGTNmlPv8+++/p02bNrRp04YuXbpw6NCh65+FhITQ\nunVrYmNja12t6e92pZJyuZi3hkeXqd1bV/BwUvL+yBiOXyhgvpWMhrdjxW97effD1Rw9kcmFrHzW\nbDjKhOe/Jfuy/dIw1BfOZBfy1dazjG4fRFxI3dm5XkMQBF4bFgFmGcbU8oZ1ral84SpLRIb4Mn18\nb9QqBS5OKpw1SnwbuzLnldFVKnDVsXMYr745Av/A0qhkT08XJj7Vh3vHdqz079M2PpRJ0wfz4KRe\nNKnn9cyvUWP/LJPJxJQpU1i/fj1BQUHEx8czfPhwWrVqdb1N8+bN2bJlC56enqxdu5ZJkyaxe/cN\nL4RNmzbh7V27Arvyiw18tjGZ7uHe9IpwXKBKTRkQ3YQBMY2ZvfEk552+ppmPkj5+I2nl3sGq45Ro\n9Xz9/Ta0NxkCTSYzxSV6vv9pN1Of7GfV8eozNxumXx3c0tHiVJsOQT54hxSQc64x5rzLyBqV7iYV\ngow+/pV39hjRszX9O0ZyODkTF42K6Bb+1YoP6NazJd16tkQUxVpv7K8t1HgHsWfPHsLCwggNDUWl\nUjF27FhWrlxZpk2XLl3w9CzVuJ06dSI9vfLGJUcxd/NpCrQGXhvs+HQGNSFXn41H5DfIlTo2bm/J\nucJkvkv5lG3ZCVYd53zGFYtRziaTmf2Hz1t1rPrONcP0iwMi64xhuiK+GNUDmZMWY2pTRJOAk1yJ\nl9qFqa16V+k+zhoVnVqH0Do8oMbBY3X5fbY3NVYQGRkZBAff2EIGBQWRkZFRYfuvv/6awYMHX/9Z\nEAQGDBhAhw4dWLBgQU3FsQppucV8sz2Fe9sH0SqgbkeEbsz6BUFVQGz7PeRe9uF0ciQGUcfai8sw\nmMun064ujRs5YzRa9kzxtXGhlfpEka7UMN3K350HO9bOgLiq0ME3mLlj4hF1apoVtOHFmH6s6f80\n3prq1WqQsC81VhCWArEr0tCbNm3i66+/ZubMmdevbd++nf3797N27Vrmzp3L33//bbHvggULiIuL\nIy4ujuzsqvlSV5X/rjuJTAbT66Bh+lZOFyZhxkxwsxT8mmSSdCQWnbZ0VZqju2i1cXy83Iht3bSc\nQVGjVvDg6LusNk5957phemTdM0xXxOCopoyJC+LsGSV3ubbEVVm3d0UNiRo/gUFBQaSlpV3/OT09\nnYCAgHLtDh8+zMSJE1m5ciVeXjdKRl5r6+vry6hRo9izZ4/FcSZNmkRiYiKJiYn4+NjOJnDg/BVW\nHcpkUvdQmnjYLr2vvWikKv2uBQHatt+L0ajg2JFYTKIJN6V10wi/8/LdxLcLQamU46RR4uqiZuqT\n/WjXuu6vhO3B6UuFfL3tLPd2CKpTLtWV4dXBUbio5Ly3OsnhGV8LCkrYs/csJ5MvOlyW2k6NjdTx\n8fEkJydz7tw5AgMDWb58OUuXLi3T5vz589xzzz189913RETcME4VFRVhNptxc3OjqKiIP//8kzff\nfLOmIlUbURT5z5rjeLuqmdSzhcPkqCz5JVo+37iLhKOnUMnl3Bvfmke7dUB1U7W1Pr4jOF+UjEHU\n4+6RT2jYKc6ejmBgOyWuCuse/bg4q5nxf/eQl19MXkEJQf6NUDTwym+Vpb4YpiuisYuK5/tF8N7q\nJDafzK50iVxrs2TpDr5btgOlQo7JLOLj7casD+7Hz1c6BrVEjXcQCoWCOXPmMHDgQKKiohgzZgzR\n0dHMnz+f+fPnA/Duu+9y+fJlnn766TLurFlZWXTr1o22bdty1113MXToUAYNGlRTkarNumNZ7E25\nwgv9I3Ct5ZlQdQYj989bxrLdh7hUUET6lQLmb9rNs0t+L9Mu0q0tIwIfRSNzRiXT0KbNUdRKkcMH\n4my2emrk4UxIsJekHKrAmiMX2XY6h5cGRuLtWj+PYMZ3akZzbxfe+yPJbnE5N7N77xm+X74Lvd5E\nUbEerdZARuYV/vXmT3aXpa4gZXP9B73RzIBPtqCQy0h4vnutP/9duT+J937/i2J92TQEGqWCJZPG\n0CqwbI1go9lIrv4SLgo3VuzK4d3VSSx8NI4+Le1XS1jCMkU6I/0+3oKns4pVz3ZDbuUUz7WJDUlZ\nTFycyNt3t7J73YiX//UDe/eVT66nVitYMOdRmjb1stCrfiFlc60mS3eXBsX9a0jLWq8cAPanZpZT\nDtc4kp5V7ppCpsBXE4CLwo3xnZsR4uXMzLUnMd0hUZmE7bnZMF2flQNA3yhfurTw4tONyRRo7Vui\ntKCgxOJ1uVzG1UKtXWWpK9T+mdAO5JcY+HRjMl1aeNE70jFno1WlqZcHagtHOHJBIMDz9uepSrmM\nlwa25GTWVX7eX/tjUuozpy+VRkzfVw8N05YQBIF/DYkir8TAvE22j+6/mW5dwlEoyk95olkkPEza\nSVtCUhCUFmPJKzHwryF1JyhuZPtoFPKyCkIuE/BwdqJL2J29hoa0bkLb4EZ8sv6UlBLcgcxYewIn\nlZxX6oFhOjElnYmLfqH/h18zbdlqkrNyLLaLCfRgZGwgi7af40K+5VW9LQgI8sRoMnNtz3ztvwMH\ntK5TRX/sSYNXEOlXilm4/Ryj2gUSE+jhaHEqjZerM99MvJdQn8ao5HKUchmxTQP4btKYSuWoEQSB\n1wa35EK+lkXbU2wvsEQ5ElNy2XA8i8k9W9R5w/TGpNNM+uZXdpxOJeNKAeuPnWbs58tIyrxksf0L\n/SMQRZi93n7p6Bd9vx2zDEThH+UggFkOuw7U76I/NaHBq80P151EgDqZrTU60I/V0x4h+2oRSrmc\nRs5Vi9voFOpFn5a+zNt8mrHxwXi63D7tsYT1EEWRmQkn8HFT81jXEEeLUyNEUeT9VZvQGm7k4TKL\nIiUGIx8lbOXrCaPL9Qlu7Mz4zs1YtP0cE7s3t0uN7fTMK6UBQfIbuweAzAt5Un6mCmjQO4jD6Xn8\ndjCTid2bE9DIydHiVBsfN5cqK4drvDKoJUU6I3M3nbayVBK3Y9PJS+xNucLzfcNxruPHG4U6PZcL\nLVd3O5xecbT+lN5hOKsUfPjnSVuJVgYvTxeL1xs3cpGUQwU0WAUhiiL//uM4Xi4qJteBoDhbEdnE\njdHtg1i8K9Wu58ENGZNZ5L8JJ2nm5cz9tbjGdGXRKBUoKjjW9HJ1rrBfYxcVk3qEsu5YFgfOX7GV\neNd5ZFxXNLfWhFAreHhcZ5uPXVdpsApiw/FL7D6Xy9T+EbhpypcTbEg81zccURT531/SLsIe/H4o\ngxMXrzJ9QCTKOuBSfSeUcjn3xbdGoyw7+TopFUzqEX/bvo93a46Xi4qZCSdsnvZi2KA2PPFID9xc\nNSgUMlxd1Dw+vjsjh7az6bh1mbq9t60mBpOZD9Yep4WPC2PrwQqupgQ3dmZsfFOW7TnP5B4taOpV\n8apPombojWY++vMU0QHuDGvt72hxrMaLg7tTYjDw+8HjKGUyTKLI4z3iGdUh+rb9XNQKnu0Txtur\nkth2Oofu4bbLsyYIAveOiOOeuztQVKzDxVltMXV4ekYuP/62j5S0HGKiArnn7vZ4NW6Y2WcbpIJY\nvuc8Z7OL+PLhuHqxgrMGz/QJ44fENGZvPMXHY2JrdC+jycyi1bv5YeNBirR6WrfwZ/q43kQ0rbuF\nl6zFir3nSb9SwvsjY2pc16A2oZTLeXdUf14a3INLBYUENHLHSVW5nfm4jk35cus5PvzzFN3CvG1u\nD5DJBNxcLdvsDh1N4+U3fsJgNGIyiRw7nsnKPw7y5WcP49/Euskt6wINbna8qjUwe0MyHZs3pl9U\n3QiKswd+7hoe7tyM3w5kcPpSzUqE/vubP1m8di95hSUYjCb2n0zniQ+Wk34pz0rS1k1K9Cb+99dp\n7gppTM86XKXwdrhp1LTw9aq0cgBQK+Q81zeMQ2l5bDxu2S3WXsz6bB1anQGTqfS4y2AwUVSsY/7C\nLQ6Vy1E0OAUxf8sZLhfpeX1o3QmKsxeTe7bASSnnkw3V903PyS/iz90n0erL1hzWGYwsWWfd/Fl1\nje92pXDpqo7pAyKkZ+8W7mkfRIiXMx+tP4XZQelfrhZquXCh/CLGbBbZeyDF/gLVAhqUgsjMK+Gr\nrecYGRtAm6CGt128E16uaiZ0a84fhy9wLDO/0v0uXy3m3R820PPN+Yz+8DuMmrJ+5lDquZN0rnyO\nqIbCVa2BzzefoXu4Nx1D639SuKqilMuY1j+C4xcKWHP0gkNkUKkUFSpuF+eGGSPUoBTE7A2nEIEX\nB9a9oDh7MbF7KO4aBZ+sP1Wp9sU6A+M+Wcpve49xpbCEK0UllMjNGG5xOZfLBMKD6/axSlpOHqcy\nczCZq56qetH2FK4UG+pkQKa9GNYmgAg/Vz5efwqjA9KBq1UKenSNKFcVUa1WcM/wDnaXpzbQoIzU\n0/pH0DPClyBPyUunIjyclDzZswWz1p1k//krtG/qedv2a/efIL9YW/aFFkBUCJjlIrJ/0jwpFXLG\nD4qzoeS243x2HlMX/U765XxkgoBapeCDBwfTJbJZpfrnFxv4cutZ+rfyo22wtHOtCLlM4IX+EUxe\nsp+VBzMZ3SHI7jK8+OwAcq8UknTiAgqFHL3BSO9ukYwZWTef3ZrSoBSEv4cTQ9vU3Yhpe/FolxAW\nbjvHx3+eYsnEjrdteyAlkxILaccVcgGFSkAsMRPR1IeXH+pLiH/dy1ZqMpt5fN6PXCoo5JqbfrHe\nwNSFv/PrKw8T2PjO+bu+3HqWq1ojL/SPuGPbhs7A6CbEBLoze+Mp7m4bgMpC9lVb4uysZvaMcaSm\nXeZiVj7NQ3zw9bZ9GpDailW+/YSEBCIjIwkLC2PGjBnlPhdFkeeee46wsDDatGnD/v37K91Xwv64\nqBU81asF207nsPPM5du2DfHxtJh2XKVU8NnUe9j51VSWvD2eNmHl65TXBXYnp1Go1XFrDJfJbObn\nnUfu2P9yoY6F288xrI0/Uf61s6zljsQzvPD2j0x8cTHf/biT4hK9w2QRBIHpAyJJyy3hh8S0O3ew\nEc2CvegYF9qglQNYQUGYTCamTJnC2rVrSUpKYtmyZSQlJZVps3btWpKTk0lOTmbBggU89dRTle4r\n4Rge6tSMJu4aPvrz5G0jXEd1jLGYdtzH3YX4FsGVyixbm8kpKMKSU43BZOZi3p3dgb/4+yxag4mp\n/Wrn7mHR8u28NWsVew+mcPJ0Ft/8uIuJ0xc7VEn0ivAhrpknc/46LaWidzA1fnv37NlDWFgYoaGh\nqFQqxo4dy8qVK8u0WblyJQ8//DCCINCpUyfy8vK4cOFCpfpKOAaNUs4zfcJITL3C5lPZFbbzcnNm\n4ZT7CPf3RiGXoZDL6BjelEVTxtSLQLDYkADMFozSTiolne9gg7hUoGXxzhRGxgYS5lv7InHzCor5\n7ufdaHU3jgj1eiOXLl9lzcY7745shSAIvDAggosFWpbtOe8wOSSsoCAyMjIIDr6RriIoKIiMjIxK\ntalM32ssWLCAuLg44uLiyM6ueMKSsB5j4oIJbux0x11EVJAvP780nk1vP8m2959i/pP34O1uOXNm\nXaOpTyOGtG+J000ZV9UKOYGN3RkYe/tdwbzNZzCYRJ7vF25rMatF0qkLqJTljwd1OiM7Es86QKIb\ndGnhTedQL+ZuOkOJXtpFOIoaKwhLE8etvsQVtalM32tMmjSJxMREEhMT8fGp2+6SdQWVQsbzfSM4\nmlFAwqHdiNp1iKbMCtt7uGhwVlfsL37i/CVmLPuLNxYlsPngmWq5izqCt8b05/XRfWndtAlhTbx4\non9Hljw/FpWiYh+PzLwSlu4+z30dgmjmVTuVZSN3Z4tBaTKZgHctyD00fUAEOYU6Fu9McbQoDZYa\nezEFBQWRlnbDmJSenk5AQECl2uj1+jv2lShPTm4h67ceJ/+qlvi2zWgfE2yzyNyRbVR8vjGXj//M\nop/fXOSCDtFpJIL7uwhC5dcXyzcd4NNftmEwmTCbRf46eJr2YYHMnjKi1tspZDKB4fGtGB7fqtJ9\n5mw6jYjIM33CbChZzYgKb4KXpwuZWfllFIVSKWf0EMdnOI0LaUyPCB/mbznDg52a4apuUE6XtYIa\nv5nx8fEkJydz7tw59Ho9y5cvZ/jw4WXaDB8+nMWLFyOKIrt27cLDwwN/f/9K9ZUoy+4D5xg75Su+\nXLqNJb/s5tUPfuXl//xqs8AiWcE0pnb6g+RcP1afDAf0ULIKseSnSt/jSmEJs3/eis5gvD4RlegM\n7E/OYPMh+xautwdpucX8sDeNsfFNa3XMjSAIfPLOGEKCvNCoFTg7qXB2UvHS5AFEhjVxtHgATO8f\nwZViAwu3SWVBHUGNVbJCoWDOnDkMHDgQk8nEhAkTiI6OZv78+QBMnjyZIUOGsGbNGsLCwnB2dmbR\nokW37SthGYPBxFsfr0aru5HnqERr4MDRNDZsPc6gXtb97kRTDhgOMTjcQEvvPszeNYihEQdRyEqg\n+DtwHlOp+ySeTCsNOjKWPUsu0RvYuD+Zvu1q5xl9dfl0YzJymVCrdw/XaOLrwbefPUZq+mUKi3SE\nNfdFXYsq3LUNbkS/KD++3HqWRzqH4OHcsGu32BurPAlDhgxhyJAhZa5Nnjz5+v8LgsDcuXMr3VfC\nMknJFyyeGWt1BhI2H7O6gkAsBuTIBD1TOyUwefXj/JwUz/0xu8FcWOnbaFQKLB2AyQQBF039ynFz\nKusqv+xPZ0LX5vi5V68MrCNoFlR780O90D+CIZ9t5cutZ6U0OXamdh/+SpThdm6jclvUtZAHgaw0\nUKh/i6O08Uvlf7sHoDNqQDOg0rfp2LKpRdlVCjkjusRYTdzawH8TTuKiUjCld+3fPdQVWgW4M7S1\nP4u2n+Nyoc7R4jiMYoOBM1dyKdLbL0ZFUhB1iKhwf4tuiRq1kqF9W1frngaTiR0nU9lwOJn8Ym2Z\nzwRBhuAxE9AgCAqmd1lL5tXGLD/WF8H1yUqPoVIq+OyZkbg6qXHRqHBWK1Ep5Dw1vAsxzWvHWbc1\n2JuSy4bjWUzu1QJPl/q1M3I00/qHU2IwMX9L/bNZ3QlRFPnvjq10+GoeI1YsocNXn/Pe1k128QKs\nPYeNEndEIZfxwasjmf7ez4iiiNFkRiYI9OocTu/OVY/UPZZ2kclf/orBWPqgGU0mpg3rzoPdb3iw\nCOqu4P07YvH3dAtPo2MzPXP3Dub+3u5UJQNy29AANvx3EjuPp1KiM3BXZFMau9deA25VEUWRmWtP\n4OumZkLX5o4Wp94R5uvGqHZBLN6ZyuPdQmniUXeO72rK1wf28c2h/WiNN2yPy44exkOt5rm7uth0\nbEG0daVwGxAXF0diYsMtPlNcomfLrmQKCkvo0LoZYSFVjwsxmEz0eXsBebfsGjRKBd9MuY/oYMsr\n+8SUXO6dv5NXBrXkqV4tqiV/fWR9UhZPLE7kP6Na80DHpo4Wp16SlltMn482c2+HYD64p3o75rrI\nXV9/TnZxcbnr7io1h558pkr3qurcKR0x1UGcnVQM7h3N/XfHVUs5AOxJTsNgwTVWbzTx066jFfaL\nC2lMr8hS3/QCbfksrg0Ro8nMfxNOEOrtwpg4+6eobigEN3bmgbua8kNiGik5RY4Wx25c0WotXi/Q\n6zDbeH0vKQgbo9cb+WvjMb7+agvr/zyCTlc7JtUinZ7ydd/ALIpc1d7eEPjigEjySwx89bdj0zHU\nFn7Zn0HypUJeHhSJwhbOAhLXmdInDJVcxseVLGhVH4jytrwIbOHZGJmNS9dKT7MNyc0t5JHxX/Dx\nRwks/X4Hn85ex/gH55OdXeBo0YhvEWxxB+GkUtKv9e09cGICPRjaxp+vtp3jUoHl1U1DQWsw8cmG\nU8QGN2JgdP0xuNdWfN00PNY1hN8PZZKU6fj3yB680b0XToqyruIahYK3evS2+diSgrAhc+ds4PLl\nQkr+SZ1cUmLgypUiZn+yzsGSgaerE1OHdEOjVFxfhTiplMQ09aNf6zsHrr00IBK90czsjcm2FrVW\n8+2OFC7ka3l1cEubpTuRKMuTPVrgrlHw4Z8nHS2KXYgPCOKH0WPpExJKoJsbPZuFsHTUfXRvGmLz\nsSUvJiuTm1vEsaPpuLlr2L7tFKZbVulms8jePWcRRdHhE8r4nu1pG+LPz7uPcrVEx4A24fRrE16p\nY5IQbxce7NiUJbvP83i35rTwcXxyN3uTX2xg7qbT9I70oVNo7Q00q294OCuZ3KsF/004yd6UXOJD\n6l6lwqoS4+vHV3ePsvu4koKwIou/3caypTtQKOSIlKbGsERtWmi2aeZPm2b+1er7bN9wftqXzn8T\nTvDF+IZXs3feltNc1Rl5eVBLR4vS4HisS3O+2Z7CB2uO8/NTXRy+2KqvSEdMViJx71lWLN+FXm+i\nuFhPSbHlaEe5XEaXLuH14oH2dlXzZM8WrDuWxb7UXEeLY1cu5JfwzfYURrULrLWlROszTio50/pH\nsP98HuuOZTlanHqLpCCsxMqV+9FacPsUBFCrFcjlMpycVPj5efDc1IEOkNA2TOzeHB83NR+sOXHb\nokL1jdnrkxHF0jxBDZ2rV7Ws+GkPb77/KwsXb+Xy5crn6aoJ93UIooWPC/9NOGHR4UKi5khHTFai\nsNCyN4+Ts5pxYzshV8gIDvaiY6cWtsmb5CCcVQqm9gvn9V+Psj4piwENwJMnOesqP+5LY0LX5rU6\nnbc9yLpUwJPPfkuJVo9OZ2Sn8gw//ZrIp7MeIDzMz6ZjK+QyXhscxcTFiSzbc56HO4fYdLyGSP2Z\nqazMhax8Xn3/F/qO/phB93/Kx/PX37aQe8+eUagtFDQxm8zcc28894/tRJeu4fVKOVzj/rhgQn1c\nmJlwwmZ1KWoT/10nJeS7xvyvNlFwtQTdPynoDQYTxSV6Zn2aYJfx+0b50im0MbM3JEuBmzag/s1W\nVuBqoZYnp3/HrsSz14pykqcAACAASURBVB/4P9Yf4cW3fqzwGGXwkDYEN/VCoynNVy+TCajVCp6b\nOvD6tfqKQi7j5YEtOZNdxA+J6Y4Wx6YkpuSyPklKyHeN3YlnLaagP30my+KRq7URBIHXh7Qit0jP\nvE31O5Hf5UIdD321m+MX7Bf/USMFkZubS//+/QkPD6d///5cuXKlXJu0tDR69+5NVFQU0dHRfPrp\np9c/e/vttwkMDCQ2NpbY2FjWrFlTE3Gsxrq/jlGiM5R58A0GE6fPZXM8+aLFPmq1kv/NeZhnnx9A\n124RDB0Wy//mPMzAgQ0jZ8zAaD/imnny8fpTXK2nKzlRFJmZUJqQ77GuIY4Wp1ZQUXEhmUyw2265\ndZAH97QLZOH2c6Tlls9ZVF+YmXCCXWcvo7hN2n9rU6O/4IwZM+jbty/Jycn07duXGTNmlGujUCj4\n6KOPOH78OLt27WLu3LkkJSVd/3zatGkcPHiQgwcP1prCQSfOXLy+ZS6DACnncyrsp1IpGDSoDe++\nN5qp0wbRwsZnsLUJQRB4Y1grcgp1zK2nK7mNxy+xN+UKU/tF4FyLqq45kmGD26K65btQKGR06xyO\n0kJqelvx0qBI5ILAB2uP221Me7IvNZcfEtN5vHtzwv3c7DZujRTEypUreeSRRwB45JFH+O2338q1\n8ff3p3379gC4ubkRFRVFRkZGTYa1OWEhlssuCkBwYP0PyqkubYMbMbp9EAu3nat3ydTyivW8sfIo\nLXykhHw3M35cF9q3bYpaVVrTWqNR0qK5L9OfG2RXOfw9nHiqVwvWHLnIzjOX7Tq2rTGazPzfb8fw\n99DwXB/7luetkYLIysrC3780yMrf359Lly7dtn1KSgoHDhygY8eO16/NmTOHNm3aMGHCBItHVI5g\nSL8YVCpFmYA2pUJO08DGxLQMcJxgdYBXBkWiUsh4b3XSnRvXEURR5KWfDpNTqGP2/e2khHw3oVIp\nmPHefcz/7GGmPzeQ2TPHMf+zh3Fzs3+9hkk9Qgls5MTbvx+rV26vi3emcvxCAW8Oa4WLBUcYW3LH\nJ71fv37ExMSU+3flypVVGqiwsJDRo0cze/Zs3N1LA4ueeuopzpw5w8GDB/H392f69OkV9l+wYAFx\ncXHExcWRnZ1dpbGrirubE/NnPUhsTFMEQUCpkNOneySfvH9/vQhwsyW+7hqe6xvGxhOX2Hi8fgQw\nLd6ZyvqkLF4dHEXrIA9Hi1MraR7iQ9/erWgZ6e+wd0SjlPPGsFaczLrKtztSHCKDtblUoOXj9afo\nEeHDoBj7u5DXqGBQZGQkmzdvxt/fnwsXLtCrVy9OniyfQMtgMDBs2DAGDhzICy+8YPFeKSkpDBs2\njKNHK65FcA17Fgwym0UEAUkxVAGDycyQT7dSYjCxflpPnFT2O4u2Nscy8xk1dwfdw7356pE46Tmw\nM6Iosud0GmsPnkQuyLi7QxSxzSvexYuiyGPf7CUx5Qobp/fEz71uV557fvkB1h65yLppPWj+/+2d\neVxUVf/H37OziAooOICCLCKKiHuauWv6pJhbrmmrS5b1tJg9PfVYWZq2WGmLlYVWmuaCuSvuu6K4\noCIiKAKyigoyzHZ/f5D8xBlUZDbwvl8vXy/mzL33fDwzc773nvNd6rlW+Xo2LRgUFRVFdHQ0ANHR\n0QwcONDkGEEQeP755wkLCzMxDpmZmWV/r1q1ivBwxytgL5VKxEmhkihkUj56MpzLV4v5dsd5e8t5\nYIpK9Lyy5BjurgrmDGspfg/swId/xfLKwhhWHDjF8gMnePGHFXy1bk+Fx0skEj6Iao7WYOTjddV7\nw3pfci4x8RlM7BpoEePwIFTJQEybNo0tW7YQEhLCli1bmDZtGgAZGRllHkl79+5l8eLFbNu2zcSd\nderUqbRo0YKIiAi2b9/Ol19+WcX/joij8EigJ4Nb+fL9zmSSsm7YW84D8b81CaTkFjF3eCs8xJgH\nm3Pq0hXWxp2hWFvqUSgIoNHpWbzrKKk5Fe9X+nu6MqlrEGuOZ7A7ybrL0dZCqzfyfkwCDT2cecmO\nAZlV2vHw9PQkNjbWpN3Hx6fMCHTu3LnC4LLFixdXpXsRB+fdJ8LYnpjN2ytOsHxiJ2Q29N+uKquP\npfNX3GWm9AyhY5CYytse7Ei4QIne1N1cAHafSSGgvnuF507qFsTfJzJ4Z+VJNr3Wxeabu1Xl5z0p\nnM8uZOEzbXGyobvwnYjuGCJWw7OWivcHNOPopQIW70+1t5z7JjW3iHdXnaR9gAdTeojpNOyFs1KO\nXGo6RUklEpwUd5/wnRQyZg+JIL2guNoVFkovKObr2CR6N/OmR1P7xlKJBkLEqjwZ6UuXJvWZvSmx\nWkS5avVGXllyDLlMytwRkaJL631gNApczS+kxMIR9H1bhZqtuSzAfVU9bBvgwdhH/Pl1XypxFx3D\nhf5eCILAe6tPISDwfv9m9pYjGggR6yKRSPhkUDhSiYQ3lx83m7fHkZi98Swn068xZ2gEPnWd7S3H\n4dm9/QwjB3zJmEHfMOTxz/j8k7/RmstC8AD4etThf8N6o5LLcFUpcFUpcVLImT2mH+617u+zeatv\nU3zqOPPGsngKLaTLmiyPu8y2s9lMfbwpDT3snym4ei3MiVRL/NxdeL9/M6auOMHCvSm88FigvSWZ\nZdvZLH7ak8K4jv4PRdryqnLq+CVmf7C6XFqa7ZtPodXoeOfDwXc9V6vTs2tfEimXcvH386Dro6Fm\nsxcMaBtGl2aN2Zd4EalUQufQAFyd7t9hoJZKzpfDIxmxYD//i0ng86da3v9/0MbsScrlgzUJdGjs\nwTOdAuwtBxANhIiNGNbWj82ns5i9MZFOQfVo5uNYVdiyrmt4c/kJwtS1eedfYfaWUy3449c9JjnL\ntCV69uw8y7WCm9Spa/4OOO9qIRPf/J3rN4op1uhwdlLw/aJdfD9nDF71TPMM1XFxol+r0AfW2b6x\nBy/3COHr2CS6NKnHwEjfB76WNRAEgeh9qXy07gzB9Wsxd0QkUgdx6BCXmERsgkQiYfbQCOq6KHhl\nyVGHetw3GAVeWxpPsdbAvFGt7Oo1Up3ITDe/rq+Qy8jLrdi1+esft5GbX0jxP3sWxRod+VeL+OL7\nLVbRCTClRzBt/N3576pTDrUXptUb+c+qk0z/+zTdQ71Y8VIn1HUcZ2lTNBAiNsPDVcncEZGk5Bbx\n9ooTDlOi9Nvt59l/IY8PBzYnqH4te8upNoSF+yGVmd7pGowCat+KXVD3HjyP4Y5cSUajwMEjF6z2\nnZDLpMwdHgmS0uhkRyhslVdYwpifD7LkUBovdQtiwdNtqOVg7riigRCxKZ2C6vHW401ZdyKThXtT\nK3XuwYw0+q9YRPCPX9B+8XcsPBlX5QnlcGo+c2OTeDLSh6FtxCytlWH0s51RqRTlklo6OSkYMfZR\nnJ0r3ieoMCLdypHqDT1c+GRQC45eKmD2Jvu6vp69cp2B8/dyPK2Ar0ZEMrVvU4dZVrod0UCI2JyJ\nXQPp08ybmevPsPPc/UW6Hs/OZNyGFZzKzUZvNJJ9s4g5h3bz5ZG9D6yj4KaWV5ccw8/dmRmDWoip\nNCqJb0NPvvn5OR7p3AS32s40CqjHK2/1Y9Qzne96XrdHmyCXl5965DIpnTsEW/0zGNDSh6cf8WfB\nrgusOmaf6oebE64w5Nt9aPVGlk3o6HB7IrdTpWR99sKWyfpErMN1jY7hPxwgObuQr0e2umemynHr\nV7AzLcWk3Vku59i4yTjJK1fWVRAEJiyOY3tiNismdSLCr26lzhd5cK5dL2by23+Qm3+DEq0BlVJG\n3ToufDd7NO51rZ9zSKs3MnbhQeIuXuXXZ9vRruEFdLoE5HJ/lKpuSCTW2YMSBIFvdyTz2eZEInzr\nsGBsW5snE6zs3OlYC14iDw21nRQsffERnv31EJP/OMpnwyIY1KriJZ7EfPNPGhIkXCkqJKBOxWve\n5vjtwEU2n87iv0+EicbBxtSp7Uz0vGc5eDSF1Eu5NPLz5JG2gTYLSlTKpfzwdFuGfbeX8Yv2sGDo\nFwR5XkYikSOVeuBRfzUymdqifWp0Bqb+dYI1xzMYGOnDp0MiqoUzhLjEJGI36rgoWPx8Bzo09uDf\nfx5n8YGLFR4bVNd8JT+jIODtUrmN5dMZ1/lo3Rm6h9bn+c6NK3WuiGWQyaR0ahfEqCEd6Nwh2OYR\n63WcFcwbeggXxU1ei5lAxjU3BKEIgyGDa1f/bdG+rlzT8NQP+/n7RAZT+4Yyd3hktTAOIBoIETvj\nqpKz8Jl29Arz4r3Vp/h+p/l61q+3fRQnefkHXme5nLHhrXBW3P/y0k2tnpeXHKWus4LPrJDCO6+g\niL93nGT9rgSuF2osem0Ry1JX8TtfRM2lxKDgpVVvcKnACzCgLdmH0WgZV9j4tAKi5u0hObuQBU+3\n5aVu1t9nsSSigRCxO04KGd+NacOAlj7M2nCWzzYlmngntWngyw99BhL4z1JSbaWKlyI7MK1Dl/vu\np1hr4LWl8aUpvEdE4llLZdH/x8ot8Qx+9Ue+jN7OZ7/GEvXyD2w/dM6ifYhYDgE9IfXS+XrglxTr\nVDz357vsS71Vk8ZQ5evHxKfz1A/7UcqlrHipE72b2Tfx3oMg7kGIOASKf/zUXZUy5m0/T2GJnvf7\nNyvn+te1YWO2jXgeoyCYTeJ2N7Kva3hx0RFOpF/j/f7N6BRUz6L6L2Xm8/VvO9HqDNw+uXzw7QZa\nNfWjbm3759WpLhgMRs6ev4IECA1ugMxKy09OTv0pvrmUpl6X+GX4x7y9bjJv/P0KL3U+yJs+Dx4P\nYzQKzNmcyHc7kmnf2IPvRre2+M2IrRANhIjDIJNKmDm4BbVUcn7ak0JRiZ5ZQyJM6khUxjjoDUZi\nz2bzfswprhfr+WFMG6vkWdqy7yx6o2nwlUQCu+LOE9U9wuJ91kTiE9J4b1YMOl2pkVUqZMx450ki\nmlk+RsWt9ttoS3ZiNObhUzuPH4fN5ePYMczf05GUa0eZM7RlpetIFJboeW3pMbaeyWZk+0Z8ENUc\npbz6LtRUyUDk5+czfPhwUlNTCQgIYNmyZbi7m3qTBAQE4ObmhkwmQy6Xl7lZ3e/5IuVJPJHGgdjT\nKFRyuj3REh9/y94N2xOJRMK7T4RRy0nO3K1JXL5azEdPNifYyzRHz91Iy7/JsiNpLD9ymSvXNTSu\n58rCZ9rR3KeOVXTrdAaMZgyEIPDPU4XIvbh2vZi3P1xRloID4GYxvPXBX/z180TcalnWJVQq86Ce\n9w40xevQauNxkwfy/bhB/Lw3j1kbzpKcXcTsoRG0bHh/Xm6X8m7ywqLDJOcU8UFUc8Z29K9W+w3m\nqFIcxNSpU/Hw8GDatGnMmjWLq1ev8umnn5ocFxAQwJEjR6hXr94DnX8nD2schCAIfPthDFtWxaEt\n0SOVSpDJpEx8dwD9hnewtzyL8+fhS3y87gw3tQaGtvFjWNuGtG5Ut8IfnVZvZMvpLJYevsSe87kA\ndG1SnxHtGtKjqbdV7+QSzmfy8oxlaLTlc0wpFTKWfvYs6vrWMUw1idUbjjH/lx0mCQCdVApefr47\nUY/bLhPrrnM5vLH8ODk3Sugfoeb5zo2JbFjxd29/ch4v/R6HUYD5o1rTOcQxb9oqO3dWyUCEhoay\nY8cO1Go1mZmZdOvWjcRE0xD2igzE/Z5/Jw+rgTh1JJX/vvAzJcXlC7MoVXKid0yjrkfNyyOUW1jC\nl1vO8VfcZUr0Rhp5uDAw0ocm3m54uirxqKXEYBRYfSydFUfTyS/S4lvXmWFtSw2Krw1rOnz+ayxr\nd56iRKtHIpGgkMt4dtAjjBtY84y3NYhetp+Ff+zhzhlJKpXwwujOjBn6iE313NDo+H5nMr/uTaVI\nayDU241ezbxo6VeXgHquuLuUfvfWn8zkk/Vn8Pd04adx7Whcz/rBfg+KTQPlsrKyUKtLA0rUajXZ\n2dlmj5NIJPTp0weJRMKECRMYP358pc4XKWX3xhNoNaZZUKUyKYd3JtJ7UBs7qLIu9Wqp+HhQC6b1\na8qmhCxWH0tn3vbzJpOIXCqhdzNvRrRvROfgenapf/3GMz3p3akp2w6eQy6T0qdTGE0CvGyuw1qk\nnrvCkV1ncanlROfHW1Db3bITYavwhqiUCjQld9wAKeREhje0aF/3g5uTgrceb8qkbsHExKez6mg6\n3++8gMFM0auuTerzzahW1HaqXES/o3NPA9GrVy+uXLli0v7xxx/fdyd79+7Fx8eH7OxsevfuTdOm\nTenS5f7dEwEWLFjAggULAMjJub/8PZZkX+xplny/ndys64RFNmTslN4EBNvWbU0mk4KE0pqLtyGR\nYDVPD0fBzUnB0DZ+DG3jx7WbOrJuaMgr1JJfpEWjM9A1tD71HMBTJKKJLxFNHDe3zoMgCALffrCa\nzX8dxmgwIpNLWfDxGt6bP442XR68TsOdtAjzpU1Lf+KOXywzEk4qBe1bBdA81Mdi/VSWWio5ozv4\nM7qDPzc0Oi7kFJGaV8T1Yh1SqYQGtZ3oFupll5sSa2OTJabbmT59OrVq1eLNN9+sNktMfy85wE+f\nbSyruSuRSFA5K/hqyST8g213h5h06jJvjf7BpPavyknBb7v/Q63a1l9OuZSRz5e/bufY6TRUSjlR\nPSJ4cXgnlPcoIi9SfYnbnciMlxahKdaWa3d2VbLk4HRUFrxrNhiMbN11hnVbTyIBnujdgp6PhdX4\nGyBbUdm5s0qjHhUVRXR0NADR0dEMHDjQ5JiioiJu3LhR9vfmzZsJDw+/7/PtjV5n4Je5m8tNyoIg\nUKLR8dv8WJtqCQn346nx3VCq5ChVclTOCpROCt6aM9wmxiG/oIgX3v2DQydS0eoM3CgqYfmmo7z7\n5d9W71vEfmxdecTEOEDpjdLxA+ct2pdMJuXx7s35+uMRfPXxCPp0ay4aBztSpdu+adOm8dRTT/Hz\nzz/TqFEjli9fDkBGRgYvvPAC69evJysri0GDBgGg1+sZNWoUffv2vev5jkTOlWsYDaYPWYJR4PTx\nSzbXM2pyT7pHRXJox1mUKgUdezWz2eb0ys3xaHX6cuv/Wq2BIycvcSkjn0Y+5vMliVRvjGbW3G8h\n3OU9S6DV6cnNLcTd3QXnStSiFrEMVTIQnp6exMaa3kX7+Piwfv16AAIDAzl+/Hilznck6ni4mlS/\nuoW32j5ZQNUNPRn49KM27/d08hWzPv1ymZSUy3migagkV/MKid1wgvzcQiLaBNCuU7BD3i33GNia\nQ9vPoLlZ/inCYDDS8pFgq/QpCAJLVhxi0ZJ9CEKpker/eASTx/eweWK/hxlx4fgeuLiq6N6/JTvW\nHy/nQaRyUjBiQjf7Cask8QcvsPzX3eRmXad1xyCGPvMYnvUrF3wWEuBF3Kk0dPryRkJvMIrGoZKc\nPHqR/772O0aDgFarZ/3KOBqHePPpt2NROljZyfbdw3j08Rbs2XgCrUaHXCFHIpXw1ucjcXKxzl39\npthTRP++r5xH07rNJ1Ap5Ux8vptV+hQxxbG+iQ7Ky+9FIZVKiF0Tj1QqQaGU88KbfWlvQQ8Oa7L+\nr8P8MGdD2T5K+qU8Ytce57vlk/H0qn3f1xnSJ5IVG+PLGQilQkbzEDWN/TwtrtsSXCooYOa2XexL\nvYSzQsGoVhFM6tgehcx+6ZaNRoGP//MXmtviWYqLtSSfu8K6lUcYNNK2/v73QiKR8Mbs4fQf3YnD\nO8/gWsuJrv0j8fS2XvDfoqUHTNxdS0r0rFp7jBee6SI+RdgI0UDcB0qlnNc+GMTEt5/gxrWbeNR3\nQyavHvnctVo9P36xsdwmu15noKhQw58Ld/PStCfu+1penm5898FwZv+0ldPnM1HIZfR9rBmvjutu\nDelVJq/oJoOil3CjpASjIFCk07Hg4BHO5eYx78n+dtOVmpxN8U3TTd8SjY6t6084lIFIPZtB4rGL\neHjXoXWXUJpGNrJJv/lXC8226/QGSkp0yF3s79L8MCAaiErg5KK02iO1tbicmmu23aA3cnR/5T1Q\nQgK8+HHGKAxGI1KJxKFzzfx+7DganQ7jbbvqGr2e7ckXuHi1AH93++whyeVSTCL9/sFR9iAMegOz\nJkdzODYBJCCVSnGt7cycFa/SoJH1nxZDgxsQfzLNpN29rgsuztXrN1idcYxvo4jVqOPuil5nfpPd\no96Dez/JpFKHNg4AxzIyKTGYbqorpDLO5ebZRINBb2TD2nimTPiVVyb8wtqYo6j93KnraRqF7OSk\n4InBjhENv27xHg5vO02JRkdJsY7iohLys67xycSFNul/4vPdcFLJuf0rplLJeWVCD4f/3tUkxCeI\nGo5nfTdatAngxJEU9Ld5IKmcFAx79jE7KrM+TerV48DFNHR3ZFnVG43417V+8jxBEJj+7l/Ex6Wi\n+WeJLyU5h707E3l/9nDenrQIvd6AXm9AKpXS7tEQej1h+YR0BoMRqbRyT3vrf9tHyR2xD0ajQGpi\nJnlXruHZwLrjF9ZEzbzPRvPz4j0kJWfhq67LM6MepXWkv1X7FSmPaCAeAt6Z/RSfvLmUhGOXkCtk\nGI1GnnmlF20fDeHg7nNsW38ciVRCzyda0rZj9SqJeDfGtolkSfyJcgZCKZPRooE3TepbP9vmmYT0\ncsYBSvcZTp1M40ahht/X/Zv9uxIpyC8ivFUjgkPVFu3//Mk05r+9hMRjF1Eo5fR8qgPjpw/ByfXe\n6/faOzaIbyGVSip8z9KEBHkza/oQm/QlYh7RQDwEuNV2ZuaCZ8nJukZBXiENG9fHyVnJ59NXsWtr\nQpk3zf6dZ+n5REumvDPAzootg2+d2vw2cijvbtzKuZxcZFIp/UJD+KBPT5v0f+LYJXQ60+SKmmId\nJ+MvEdk6gG59ws2cWXVy0vOZOugLigtLgNIJf+uyA1y5lMsnf0655/ldB7RmxYJt6O5IvV3Ho5ZN\n9iBEHIOHwkDo9QZ+/2U361bFodHoaNW2MROm9MbH7+Hy3a/vXYf6/7gmJiaks3NLQjnvJk2xjq1/\nx9N/aDsCQyxfdc0eRKgb8PezYyjW6ZBLpTZ1b63r7oJCKcdwR3p2lUpOXQtnQr2TmJ93mkzuuhI9\nCQeTSUu6QsN7fL5DX+rJ3o3HyUm/iuamFoVSjkwu5a1vxtaYJ0yRe/NQGIhP3lvJ4f3nywqRHNiT\nxMn4S/y89CXcPaz7Q827UsCm3/eSmZJDi05N6DqoLSoH8MI4si8Jndb07lZvMHJk3/kaYyBu4ayw\nfRrmx7qH8d3XW0zapVIp3Xo2s2rfKQmXy+053UKukJF+IfueBsLVzZl5G6eyZ108J/Yl4d3Qkz7D\nH7H63oOIY1HjDUTG5XwO7TuP9rbJUBAEtCV6/l55hLEvdLVa32cOX+A/w77CoDegK9GzZ+0x/py7\nga+2vEOtOvYtYu/sqkIul5UbFwC5XIZzNXPldVRcXVV8OncUH7y7gsJCDRIkOLsoeH/GUNyslFzx\nyLYEfv5wJZfOXfl/V9rb7vj1OgONmtyf8VeqFPQY3I4eg9tZQ6pINaDGG4jUCznIFaYToVar5+yp\ny1brVxAEZk9aiKaopKxNU1RCTvpVln65kRemD7Za3/dD197h/Dpvq9n3uvRqbmM1NZemzXz5fcUr\npCRnIwgCgcHeSK1UN+DItgRmPPeDScVBBAEkEpROCtp0C8Oncc0pYlRZzlzMYtux8yhkUvq0CyWg\nwcO1zFxZanwchI+fOwa9aRyAXC4jIMh6P5Sc9KvkZ10zaddp9exeY/9yqZ713Xhn5jCcnBW4uKpw\ncVXh7KLkvdnDqWPl9fGHDalUQlCIN8FNGljNOAAs/GiVqXH4h1p1nBn4YnfeWfCC1fp3dL5YtoMX\n5izjlw2H+GndQUZ99DtLtx2ztyyHpsY/QQQEehHaTM2ZU+nobluTVShkPDmsvdX6VSjlVFSLSekg\nZQk7dm3Kn1umEn84BYlEQmS7xhYt/nI7giCIm5tWJj05y2y7VCrht/iZDrH3ZS9OpVxhxa6TaP5Z\nSTAIAgajnq9W7KZn6xDq16159dwtQY1/ggD4cM4IuvZqjkIhQyqVEBzagDnzn8bLihtu7l61CY5o\nhPSO1AkqZyVPPFO5cqvWxMlZySNdQunwWBOLGwdBEPhz41H6TfqOjmO+YOjrP7P7aLJF+xD5f+pX\n4JXnWsfFYW5K7EVs3DlKzDhlSCUSdp+4YAdF1YMa/wQBpSm7p74/kDf+MwCDwWizdMrv/PgCbw74\njBtXixCMAkajQNuezRjwXDeb9G9vFq89zMKV+8vu2i5nFfDfb9Yy+98D6RARYBMNVwuL2XEyGb3B\nQJfmgXi7Vy7FeXVi7NtRfPHqonIR0CoXJSNf72fxp7cbV4vYvHQ/qafTCW7ZkF7DO+LqZv2qhg+K\nXFZ6c2i4o8CRBAky6UNxn/xAVKkmdX5+PsOHDyc1NZWAgACWLVuGu7t7uWMSExMZPnx42esLFy7w\n4Ycf8tprrzF9+nR+/PFH6tevD8Ann3zCv/71r3v2a+ua1FXBYDByfPdZcjMKaNLKn4CwmlXQviL0\nBiOPT5hPkZlSlWGBDfjlo9FW17D5aCLv/bYZqaR0n9YoCEwZ0JkxPVpbvW97sXXZAX6ZsZqCnOu4\n1nFh5Ov9ePJFy+Yvunz+Cv/+1xy0JTq0Gh0qZyXOriq+2jQNLweNLUq6nMu4mUsouSNwUaWQsW7W\ni7g7sHGzJJWdO6tkIKZOnYqHhwfTpk1j1qxZXL16lU8//bTC4w0GA76+vhw8eBB/f3+mT59OrVq1\nePPNNyvVb3UyEA8rBTduMuDlBSbFhQBquajY+uPLVu3/amExfd//kZI7YgFUCjl/vDWKIHXNjQYW\nBAFdiR6FSm6VfZ+pT37BqQPny+2xSaQSOvVryX8XTrB4f5YietNhvl+zHwmlNS4EQWD6M4/Tp131\nqOtiCSo7d1ZprSUmJoYdO3YAMG7cOLp163ZXAxEbG0tQUBD+/g9vwq1reTfY/Nse0hIzaNouiB5P\ndbyv3DjVjVou27OA6wAAFjJJREFUTqgUMrMGwl/tbuYMy7LjZDJSM5Oj3mBgY9xZJve3fclWWyH5\nx6XVGhgMRk4dPG/igCEYhdLU4JXkwPYzLJq3laz0AgJCvHn2tT6EtwmwkNryjHu8HX3ahrL7xAXk\nchndI4Nwd7NvPNLtCILAtRvFuDgrUSocY/W/SiqysrJQq0sTjKnVarKzs+96/NKlSxk5cmS5tnnz\n5rFo0SLatm3L559/brJEdYsFCxawYMECAHJycqoi226kJKTx5uMz0Wn1aDU6dq06zJLZf/P1zvdx\n96pZEapymZRnBz3Cjyv2obkt5YNKKWfiU52t3r/eYDBbcsEoCOgrqDEucm8kktKaFXqjmTTqyspN\nJ9vWxvPV/1aXpXtJOHqRd8f/yowfxtGibWOL6L0TtWdtnuoeaZVrV4VtBxL5cuF2rhdqkEjgie7h\nvPZMdxR2Lkx2z92ZXr16ER4ebvIvJiamUh1ptVrWrFnDsGHDytomTZpEcnIy8fHxqNVq3njjjQrP\nHz9+PEeOHOHIkSNlexbVjc8n/UzR9WK0//wgNP/k2P9l+l92VlYxaam5LJy3la9nruXwviSMxvuf\nXEf9qy1TRnWlnrsrUqmEAB8PZr4aRbtw6z9BdmkeWK5Q0C1UCjk9I0Os3n9NRSqV0nlAK+SK8hOX\nQlWaLfZ+EQSBnz4rX+kQSrPd/vTZRototTaCIJBw8Qp/HzhNQuqVCt3a78Wx02l8NG8jeQVF6PQG\ntDoD63ckMPtH0zQttuaeJn/rVvPRtgDe3t5kZmaiVqvJzMzEy6viwLMNGzbQunVrvL29y51/ixdf\nfJH+/e1XBtLa3LxRTMop0wpZBr2BfeuO8bodNN2LzX/H882stRj0RgwGI7HrjxPZrjHvzxlxX5XP\nJBIJg3tFMriX7e/YvN3dmDKgM9+s3YveYMAoCKgUcgZ3akG4f83KM2VrXpo5gkvnrpCRklOWziOo\nRUOe/c+T930NzU0t1/KLzL538bz5eA5H4qZGy+T5q0hMyy7bzwjxrc+3rwzG1aly8Sa/rjxg4oJb\notWzZc9ZpozthpurkyWlV4oqLTFFRUURHR3NtGnTiI6OZuDAgRUeu2TJEpPlpVvGBWDVqlWEh1sn\n9bEjIJPLyuXEuZ3KPprbgqJCDd/MWov2tuUhTbGO+MMp7N95ls49rJtszhKM6dGajmH+bIw7i95g\npGdkiGgcLIBbXVfmbf0Ppw9f4PL5LALCfGgS6V+pDXGVswKVs4KbhSUm73l61bakXKvw5apdnL6Y\nhfa2PbYzadl8vmIn74/uXalrXb5SYLZdLpOSd7XIrgaiSg7A06ZNY8uWLYSEhLBlyxamTZsGQEZG\nRjl31Zs3b7JlyxYGDy6ff2jq1Km0aNGCiIgItm/fzpdfflkVOQ6NyllJ6+7Nkd3xaK50UvD4045X\n2e34kdTS2sl3oCnWsWPTKTsoejCC1J5M7v8orw58TDQOFkQikdC8fRCPj+pEaKuASntLSaVShjzT\nGZVz+c10lZOCMZN7WFKqVVh38Ew54wCg0xtYf+hspa/VLFht1qHCKIDazsaySreunp6exMbGmrT7\n+Piwfv36stcuLi7k5ZnWAF68eHFVuq92vP7tc7zVbxZ5mQUI/6zlN20XxKipUXZWZopCKQNMv7QS\nCVZLxyHycDFyQjeMBiMro/ei1xtwclYy7pXedH/C8TaR70RrJr8blBqJyqaVeX5oR/YdvYBGo+PW\nLoaTSs4zgzugUtr3t+Z4axs1GHevOiw4/DEn9ySSmZpDUItGhLQKsLcss7Rs29jsiphSpaDvwFa2\nFyRS45BKpTz9ci9GTuhOUaGGWrWd72tvyxHo0LQhB85cKucIIZFAu9CGlX6aCvDzZMGMkcz/bRcJ\nSZl41HFl7KD29O1i/2XcKgXK2QsxUM42nIq/yH+n/A6UemwYDQLDxnZi7ETHXwIQEbEmaTkFPP3p\nEjQ6PSU6PSqFHJVCxqKpI/H3sn6cz4Ni00hqe1HdDMStIa6O2Uw1xVoO7jlHcZGW1o8E4tWgrtnj\nbt4sIWb1UfbsSaRObRcGD2lL23aBNlYrImI7rhVpWL3vFGfTsgn18+LJTs2pW8uxU3bYNJJa5O6k\nn7/C168s5MSuM8jkMro91ZFJnz2Nq52ryVUGJ2clXXvf3busuFjLpAm/kJ19o6ww0/Hjlxjz9KOM\nHNXRFjJFRGxOHVcnxvVua28ZVqV6LPhVQ67nF/LqY+9zfMdpjAYjuhIdO/7cx7R/zXzggBpHZf26\n4+Tk3ChXtU+j0bEoeg83bhTbUZmIiEhVEA2Eldi8aCdaja6cMdBp9Vw6m87ZQ+ftqMzy7N+fREmJ\naa59uULG2TOZVuv32o1iFq89zPvz1/PH+iNcL9JYrS8RkYcRcYnJSlw4frFcXv7bSUvMIKxDaboH\nQRC4nncDJ1enalvxy8OjFhIJJrmPjAYjdepYZ032UuZVnp/+B1qtgRKdnp1x54lec4hfPhyNTw3L\nayUiYi/EJwgrEdy6cbkJXxAEjHoDxddvsnreRo7GnuTwpnjGBL3MiIaTGOT5LJ+Om0dxNbwLHjSo\nDco7osGlUgn16rsR0sQ6wWmfLtxK4c2Ssvz+JVo9N4pK+GzRNqv0J2IZCnJvcHTnGS5Xg3QaIuIT\nhNXo83QXlsyKQVeiw2AwIvwTdSkIkBR3gfeiPsVgMGK4rV7Bzr8OUFhQxEcxb9tL9gMR1syXV6b0\nYd43W5BKJRiNAt4N6jBz5lNW8dwyGgWOnb1s+sQiCBw+ddHi/YlUHUEQ+P695Wz4bS9KpRydzkBI\ny0ZMj55IrWrktPGwIRoIK1Grrivf7PmQb99YxIG1cSbva+/IYgmg0+g4uvUk2Wm5eDWsZwuZFqPf\nv1rSo2czzp27glstJwIaWy/j7q2U00YztSbsnR5ZxDwbf9/Hpj/2oyvRo/tnvyrxWCqfv7qI//06\n0c7qRCpCXGKyIg0ae/Hhyjdxr3//+VQUKgXZF3OtqMp6qFQKWrRoaFXjAKXxJH06hpoYA4VcRr/O\n9o8+FTFl1YJtJntyeq2BI9tPU3Rd9HRzVEQDYQM81OaDy8yhK9HR6CGpW10VXn+6O0386+OsUuCs\nUuCkUtAs0JuXR3SxtzQRMxReu2m2XSqVcrOw+u27PSyIS0w2YMTbT/LZc9+hufn/qY0VKgWCsbTO\ngmAsXUxXuajoP74ntT3d7CW12uDqouKn6SNJSL7CxYx8Av08CQsUs7U6Km27NyP2r0MY76jm5+bu\nSr1K3ECJ2BbRQNiArsM6knM5j+jpy5EAep2BzoPaM2LaQBZ/8BfHd57Gzd2VIf9+ggET+5Sdp7lZ\nwrbfd3Nq71n8mqjp+1wPPBo4bp4XS6LV6Uk8fwWVSkFIYy+zm90SiYTwYDXhwWo7KBSpDE+/1Z+D\nW05RXKhBp9UjlUlRKGW89tmoapmC5mFBzMVkQ7QaLZkp2bh716W2R627Hnst9zqT20/jWs51NEUl\nKJ0UyBRy5mx9n9B2wTZSbB927j/HrK83IAil3i91ajvz6XtDaNyoem3ci5SnIPcGa37ewYn9SfgE\n1GfwxJ4ENPWxt6yHisrOnVXag1i+fDnNmzdHKpXetdONGzcSGhpKcHAws2bNKmvPz8+nd+/ehISE\n0Lt3b65evVoVOQ6P0kmJf5jfPY0DwKIPlpOXno+mqHRZSqvRUXyjmNnPzLe2TLuSlnGVGV+so+im\nlpvFWoo1Oq5kX+e1//6J3ozXkkj1oW49N8a+PYDPVr/O63OftppxSL+czzefb+TNlxfzyw/byc8r\ntOj1k1Nz+GHxLub/uoPT56yXKcARqJKBCA8PZ+XKlXTpUvHGoMFgYPLkyWzYsIHTp0+zZMkSTp8+\nDcCsWbPo2bMnSUlJ9OzZs5zxeNjZs+IAep3phJh54QpXs6/ZQZFtWLv5OAaDaTGWEq2ew/FijIPI\n3Tl1Io2JY39k3eqjHD96keV/HOD5Ud+TcTnfItf/feVBJkz9jT9WHeLPmMO8+t5SvllYc4Mzq2Qg\nwsLCCA0Nvesxhw4dIjg4mMDAQJRKJSNGjCAmJgaAmJgYxo0bB8C4ceNYvXp1VeTUKBQVVG0TBMes\nYW0p8guK0JsxEIIgcF1M/CdyD+bOWodGoyu7ydDpDBQVlvDjfNPKl5UlM+saC5fspUSrx2gUEATQ\nlOiJ2XScxPNXqnx9R8Tqbq7p6ek0bNiw7LWfnx/p6ekAZGVloVaXbjCq1Wqys7OtLafa0H98b5Pc\nTDK5lPDOTalV19VOqqzPI60DcTZjHA0GIxHN/OygSKS6cLOohMtppk8KgiBw9EhKla+/Py7ZXBVe\ntFo9Ow8kVfn6jsg9DUSvXr0IDw83+XfrKeBemNsDfxCvhQULFtC2bVvatm1LTk5Opc+vbgx9YwCR\nPcJRuShxclXh7OaEd4AXby96xd7SrErXTk0IaOiJSvX/T0lOKgUD+0ai9haT8IlUjEIpRyo1P7e4\nuKiqfH25TIbUzNwllUprbAT/Pdcqtm7dWqUO/Pz8SEtLK3t9+fJlfHxKN6e8vb3JzMxErVaTmZmJ\nl5dXhdcZP34848ePB0p34ms6coWcGX+/Q/LxVJLiLuDlX5/I7qUOATUZuVzG15+MZN2WE2zddRZn\nZwVP9o2kc4ea7bklUnUUChldeoSxa9sZdLft36lUcgYOrfqc8ViHYL7+2XS/QSaT0vOxplW+viNi\n9cXsdu3akZSUREpKCr6+vixdupQ//vgDgKioKKKjo5k2bRrR0dEMHDjQ2nKqHUEtAwhqGWBvGTZF\npZQz+InWDH6itb2liFQzprzZj7zcQs6cuoxcIUOn1fNY96YMG1n1yobudV15Z0o/Pvl6AzKpBEEA\no9HI5HFdaeTrYQH1DohQBVauXCn4+voKSqVS8PLyEvr06SMIgiCkp6cL/fr1Kztu3bp1QkhIiBAY\nGCjMmDGjrD03N1fo0aOHEBwcLPTo0UPIy8u7r37btGlTFdkiIiI1nEupucLBfUlC1pUCi1/76rUi\nYe3WE0LMpnghJ++Gxa9vTSo7d4qBciIiIiIPCTYNlBMRERERqbmIBkJERERExCyigRARERERMYto\nIEREREREzCIaCBERERERs4gGQkRERETELNXSzbVevXoEBATc9/E5OTnUr2/dOslVQdRXNRxZnyNr\nA1FfValu+lJTU8nNvf+a99XSQFQWR4+bEPVVDUfW58jaQNRXVWq6PnGJSURERETELKKBEBEREREx\ni2z69OnT7S3CFrRp08beEu6KqK9qOLI+R9YGor6qUpP1PRR7ECIiIiIilUdcYhIRERERMUuNMxDL\nly+nefPSwjp37t7PnDmT4OBgQkND2bRpU1l7XFwcLVq0IDg4mClTppitgmcNhg8fTmRkJJGRkQQE\nBBAZGQmUuqI5OzuXvTdx4kSb6Lmd6dOn4+vrW6Zh/fr1Ze9VNI625K233qJp06ZEREQwaNAgCgoK\nAMcYu1ts3LiR0NBQgoODmTVrlt103CItLY3u3bsTFhZG8+bN+eqrr4C7f9a2JCAggBYtWhAZGVlW\nFCw/P5/evXsTEhJC7969uXr1ql20JSYmlo1PZGQktWvXZu7cuXYdu+eeew4vLy/Cw8PL2u42Xg/0\nu7VstnH7c/r0aeHs2bNC165dhcOHD5e1JyQkCBEREYJGoxEuXLggBAYGCnq9XhAEQWjXrp2wb98+\nwWg0Cn379hXWr19vc92vv/668MEHHwiCIAgpKSlC8+bNba7hdv73v/8Jc+bMMWm/2zjakk2bNgk6\nnU4QBEGYOnWqMHXqVEEQHGPsBEEQ9Hq9EBgYKCQnJwslJSVCRESEkJCQYFdNGRkZQlxcnCAIgnD9\n+nUhJCRESEhIqPCztjX+/v5CTk5Ouba33npLmDlzpiAIgjBz5syyz9me6PV6wdvbW0hNTbXr2O3c\nuVOIi4sr932vaLwe9Hdb454gwsLCCA0NNWmPiYlhxIgRqFQqGjduTHBwMIcOHSIzM5Pr16/TsWNH\nJBIJY8eOZfXq1TbVLAgCy5YtY+TIkTbt90GoaBxtTZ8+fZDLSwsiPvLII1y+fNnmGu7GoUOHCA4O\nJjAwEKVSyYgRI+67jru1UKvVtG5dWqXPzc2NsLAw0tPT7arpXsTExDBu3DgAxo0bZ/PfpjliY2MJ\nCgrC39/frjq6dOmCh0f5SnYVjdeD/m5rnIGoiPT0dBo2bFj22s/Pj/T0dNLT0/Hz8zNptyW7d+/G\n29ubkJCQsraUlBRatWpF165d2b17t0313GLevHlERETw3HPPlT2qVjSO9mThwoX069ev7LUjjJ0j\njtPtpKamcuzYMTp06ACY/6xtjUQioU+fPrRp04YFCxYAkJWVhVqtBkoNXHZ2tl203c7SpUvL3cw5\nwtjdoqLxetDvY7U0EL169SI8PNzk393u0AQz+woSiaTCdltqXbJkSbkvnFqt5tKlSxw7dowvvviC\nUaNGcf36dYtpuh9tkyZNIjk5mfj4eNRqNW+88QZQ8Thag/sZu48//hi5XM7o0aMB243dvbDlOFWW\nwsJChgwZwty5c6ldu3aFn7Wt2bt3L0ePHmXDhg3Mnz+fXbt22UXH3dBqtaxZs4Zhw4YBOMzY3YsH\n/T7KrSHG2mzdurXS5/j5+ZGWllb2+vLly/j4+ODn51dueeJWu6W4l1a9Xs/KlSuJi4sra1OpVKhU\nKqDUhzkoKIhz586VbdzZStstXnzxRfr37w9UPI7W4F76oqOjWbt2LbGxsWVfdluN3b2w5ThVBp1O\nx5AhQxg9ejSDBw8GwNvbu+z92z9rW3NrfLy8vBg0aBCHDh3C29ubzMxM1Go1mZmZeHl52UXbLTZs\n2EDr1q3LxsxRxu4WFY3Xg34fq+UTxIMQFRXF0qVLKSkpISUlhaSkJNq3b49arcbNzY0DBw4gCAKL\nFi1i4MCBNtO1detWmjZtWm6ZKycnB4PBAMCFCxdISkoiMDDQZpoAMjMzy/5etWpVmadEReNoazZu\n3Minn37KmjVrcHFxKWt3hLEDaNeuHUlJSaSkpKDValm6dClRUVE213E7giDw/PPPExYWxuuvv17W\nXtFnbUuKioq4ceNG2d+bN28mPDycqKgooqOjgdIbAlv+Ns1x59O+I4zd7VQ0Xg/8u7Xsvrr9Wbly\npeDr6ysolUrBy8tL6NOnT9l7M2bMEAIDA4UmTZqU81Q6fPiw0Lx5cyEwMFCYPHmyYDQabaZ33Lhx\nwnfffVeu7a+//hKaNWsmRERECK1atRLWrFljMz23GDNmjBAeHi60aNFCGDBggJCRkVH2XkXjaEuC\ngoIEPz8/oWXLlkLLli2FCRMmCILgGGN3i3Xr1gkhISFCYGCgMGPGDLvpuMXu3bsFQGjRokXZuK1b\nt+6un7WtSE5OFiIiIoSIiAihWbNmZeOVm5sr9OjRQwgODhZ69Ogh5OXl2VzbLYqKigQPDw+hoKCg\nrM2eYzdixAihQYMGglwuF3x9fYWffvrpruP1IL9bMZJaRERERMQsD80Sk4iIiIhI5RANhIiIiIiI\nWUQDISIiIiJiFtFAiIiIiIiYRTQQIiIiIiJmEQ2EiIiIiIhZRAMhIiIiImIW0UCIiIiIiJjl/wDx\n1SFSKtLGmgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 600x400 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0nphBRRZ80Zt",
        "colab_type": "text"
      },
      "source": [
        "# Explanation\n",
        "\n",
        "Observations $s$ are scalar values between -100 and 100. Actions $a$ are scalar values between -1 and 1.\n",
        "\n",
        "The plot above shows $(s, a)$ pairs, with their corresponding targets $y$ as color (dark is low, light is hight). The high target regions follow the curve $f$, which gives the mode (argmax action) as a function of $s$.\n",
        "\n",
        "The goal is to recover $f$ from the given data points.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GFFKJaFFfcI6",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "data = (s[:, np.newaxis], a[:, np.newaxis], y[:, np.newaxis])\n",
        "s_features = tf.constant(np.linspace(-100, 100, 50)[np.newaxis, :], dtype=tf.float32)\n",
        "\n",
        "hidden_widths = [1000, 500]\n",
        "model = tf.keras.Sequential(\n",
        "    [tf.keras.layers.Lambda(lambda x: tf.exp(-(x - s_features)**2/2000))]\n",
        "    + [tf.keras.layers.Dense(w, activation='relu') for w in hidden_widths]\n",
        "    + [tf.keras.layers.Dense(1, activation=None)]\n",
        ")"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XfoYOomc9e_m",
        "colab_type": "text"
      },
      "source": [
        "What loss functions best recover the curve $f$ from our dataset?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BN6JkI2NT4yU",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# loss A\n",
        "#    ||h(s) - a|^p - R|^q\n",
        "# This is danabo's mode regression loss\n",
        "\n",
        "p = 0.1\n",
        "q = 1/P\n",
        "# p = q = 2.0\n",
        "def loss(model, s, a, y):\n",
        "  reg = tf.linalg.global_norm(model.trainable_variables)\n",
        "  return tf.reduce_mean(tf.abs(-tf.abs(model(s)-a)**p - y)**q) + 0.003*reg"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yWbSJPG4T5JB",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# loss B\n",
        "#    |h(s) - a|^p * exp(R/tau)\n",
        "# This is one of Dale's surrogate loss, specifically dot-product loss.\n",
        "\n",
        "p = 1.0\n",
        "tau = 1/10.\n",
        "def loss(model, s, a, y):\n",
        "  reg = tf.linalg.global_norm(model.trainable_variables)\n",
        "  target = tf.cast(tf.exp(y/tau), tf.float32)\n",
        "  return tf.reduce_mean(tf.abs(model(s)-a)**p * target) + 0.0005*reg"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q56RI8-V1_V8",
        "colab_type": "code",
        "outputId": "40e9b633-8516-4763-f180-4d55f137fb34",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1568423585282,
          "user_tz": 420,
          "elapsed": 293,
          "user": {
            "displayName": "Dan Abolafia",
            "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mAQmxyT8biPkQeDgz5lf2ocSzJsOqH8BqBuLz1a=s64",
            "userId": "05741471333872541970"
          }
        },
        "colab": {
          "height": 34
        }
      },
      "source": [
        "np.var(s)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "3297.3220206374854"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 56
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dn8ggwVZesaY",
        "colab_type": "code",
        "outputId": "c0c8ca98-58a8-436e-870e-bc2b920ede4c",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1568423585608,
          "user_tz": 420,
          "elapsed": 300,
          "user": {
            "displayName": "Dan Abolafia",
            "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mAQmxyT8biPkQeDgz5lf2ocSzJsOqH8BqBuLz1a=s64",
            "userId": "05741471333872541970"
          }
        },
        "colab": {
          "height": 34
        }
      },
      "source": [
        "# Initialize model\n",
        "\n",
        "device_string = '/device:GPU:0'\n",
        "# device_string = '/device:TPU:0'\n",
        "# device_string = ''  # CPU\n",
        "\n",
        "with tf.device(device_string):\n",
        "  model(data[0])\n",
        "  print(loss(model, *data).numpy())  # Initialize model\n",
        "\n",
        "optimizer = tf.keras.optimizers.Adam(learning_rate=0.0001)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.014822608\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PjqYN66ygqxH",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def sample_batch(batch_size, *args):\n",
        "  assert args\n",
        "  idx = np.random.choice(args[0].shape[0], batch_size)\n",
        "  return tuple([arg[idx] for arg in args])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "V1C8fNjNfba0",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "for i in range(10000):\n",
        "  # batch = sample_batch(100, *data)\n",
        "  batch = data\n",
        "  optimizer.minimize(lambda: loss(model, *batch), model.trainable_variables)\n",
        "  if i % 100 == 0:\n",
        "    print(i, '\\t', loss(model, *data).numpy())"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8uBenv2C9iYM",
        "colab_type": "text"
      },
      "source": [
        "Test recovery of $f$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "I8v-OUy7hD1D",
        "colab_type": "code",
        "outputId": "77c9c082-b7e6-4614-c365-c9fb9de12b50",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1568423597001,
          "user_tz": 420,
          "elapsed": 428,
          "user": {
            "displayName": "Dan Abolafia",
            "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mAQmxyT8biPkQeDgz5lf2ocSzJsOqH8BqBuLz1a=s64",
            "userId": "05741471333872541970"
          }
        },
        "colab": {
          "height": 269
        }
      },
      "source": [
        "X = np.linspace(-100, 100, 200)[:, np.newaxis]\n",
        "Y = model(X).numpy()\n",
        "plt.plot(X, Y)\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ujgN09o/gp++UQyFxxwvfTZp2m1xrogAg0wr0ccPCaD/sO9085b7OzqxQo0V8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\namGy6YUAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 600x400 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "A5Rev3QIhQFf",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}